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Not too sure if this is a realistic GMAT question because it may require trigonometry - which is not something tested on the GMAT.

However, if this were to show up on the exam - try to apply some common sense logic - but in a structure way as we always say.

You're given each side is 1 and you have various answer choices.

Well, obviously a square with base = 1 and height = 1 would give area = 1. Whats't the base and height here? Well, you can say the base =1, but then the height you don't really know.

But can you guess if the height is greater than or less than 1?

Draw it out. You'll see that the height HAS TO BE <1.

So that means the area MUST be less than 1.

Now look at your answer choices.

You've got the obvious answer choice (A) = 1. This one is obviously wrong and is the booby trap.

(B) 1/square root 2 = (square root 2) / 2 = ~1.41 / 2 = ~.7

This is less than 1 so we keep that in mind.

(C) is 1/2, which is also less than 1, but seems a bit too much less than one since the height seems to be greater than .5

(D) square root 2 = ~1.41

This is greater than 1 so is not correct.

(E) none - I don't think GMAT would give an answer choice of none.

So between (B) and (C), (B) is the better guess and is more reasonable.

So that's your answer - 1 / root 2.

See--even though I didn't exactly calculate it using trigonometry, I was able to arrive at the answer by using the answer choices as a resource to limit the scope of the problem at hand. These are the kind of test strategies you'll need to develop in cases of emergency.